The present invention pertains to particles of magnesium chloride (MgCl.sub.2) with a novel shape as well as to the procedure for manufacturing these particles. These MgCl.sub.2 particles can be employed as a catalytic support, especially in the catalytic components of the Ziegler-Natta type. The polyolefins obtained by means of polymerization of olefins in the presence of the catalytic component containing this MgCl.sub.2 also have a distinctive structure. These catalytic components and the polyolefins obtained in the presence of these components are also part of the invention.